IPod Touch will charge from computer USB, but not from AC outlet

The iPad uses a 10W charger. The iPhone has a 5W charger. Most older computers only support the original USB spec of 2.5W USB port power support. Your iPad, when on, uses more than 2.5W, so it will not charge unless it's turned off, and when off it will charge at less than 1/4 the speed of the normal iPad charger. That can be up to 16 hours for a fully depleted iPad.

Newer Apple computers, and computers that support USB3.0, support higher USB power standards, but if your computer doesn't then you'll need to invest in a new charger for your iPad.

Note that the iPad will generally charge off other USB chargers from other manufacturers, but only at a slower rate than the original iPad charger, unless the charger you use is specified to charge the iPad. When the original iPad came out 10W USB chargers were not common.

PS: when I use my friend's magsafe it charges my MacBook Pro.

Sorry if this is too obvious, but if your friend's magsafe charger indeed charges the battery without any problems, then it certainly seems like the problem is in your charger. (Somewhere in it; the cord, magsafe adapter, or some other part.)